A typical multi-stage refrigeration device includes a main refrigerant stream and one or more sub-cycle or auxiliary refrigerant streams. A multi-stage refrigeration device may have improved efficiency compared to a single-stage device because the auxiliary stream cools the main stream while maintaining the high pressure of the main stream (i.e., lower pressure on the suction side makes the compressor work harder). However, the effectiveness of the auxiliary stream in precooling the main stream depends on the performance of the intermediate heat exchanger. In this regard, what is needed is a control methodology to regulate the auxiliary expansion value that controls the flow rate intermediate heat exchanger.